• Proceeding of EDISON Challenge
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• 2015.03a
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• pp.246-250
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• 2015

In this paper, Timoshenko and Euler-Bernoulli beam theories(EB-beam) are used, and Fast Fourier Transformation(FFT) analysis is then employed to extract their natural frequencies using both analytical approach and Co-rotational plane beam(CR-beam) EDISON program. EB-beam is used to analyze a spring-mass system with a single degree of freedom. Sinusoidal force with various frequencies and constant magnitude are applied to tip of each beam. After the oscillatory tip response is observed in EB-beam, it decreases and finally converges to the so-called 'steady-state.' The decreasing rate of the tip deflection with respect to time is reduced when the forcing frequency is increased. Although the tip deflection is found to be independent of the excitation frequency, it turns out that time to reach the steady state response is dependent on the forcing frequency.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.10
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• pp.1049-1056
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• 2008

A method for the vibration analysis of curved beam conveying fluid with uniform velocity was presented. The dynamics of curved beam is based on the inextensible theory. Both in-plane motion and out-of-plane motion of curved beam were discussed. The finite element method was formulated to solve the governing equations. The natural frequencies calculated by the presented method were compared with those by analytical solution, straight beam theories and Nastran. As the velocity of fluid becomes larger, the results by straight beam model became different from those by curved beam model. And it was shown that the curved beam element should be used to predict the critical velocity of fluid exactly. The influence of fluid velocity on the frequency response function was also discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.285-290
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• 2003

A method for the dynamic analysis of curved beam conveying fluid presents. The dynamics of curved beam is based on inextensible theory and the fluid in curved beam has uniform velocity. The equations of motion of curved beam are decoupled by in-plane motion and out-of$.$Plane motion. The solutions of equations are presented by a finite element method and validate by comparing the natural frequency with analytical solution, straight beam theories and Nastran. The influence of fluid velocity on the frequency response function is illustrated and discussed.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.369-377
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• 2018

In this article, buckling and free vibration of functionally graded (FG) nanobeams resting on elastic foundation are investigated by developing various higher order beam theories which capture shear deformation influences through the thickness of the beam without the need for shear correction factors. The elastic foundation is modeled as linear Winkler springs as well as Pasternak shear layer. The material properties of FG nanobeam are supposed to change gradually along the thickness through the Mori-Tanaka model. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. From Hamilton's principle, the nonlocal governing equations of motion are derived and then solved applying analytical solution. To verify the validity of the developed theories, the results of the present work are compared with those available in literature. The effects of shear deformation, elastic foundation, gradient index, nonlocal parameter and slenderness ratio on the buckling and free vibration behavior of FG nanobeams are studied.

• Advances in concrete construction
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• v.17 no.4
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• pp.187-210
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• 2024

Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotating nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and Hamilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.519-545
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• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

• Steel and Composite Structures
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• v.19 no.4
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• pp.829-841
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• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equilibrium equations are derived from the principle of virtual displacements. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.232-239
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• 1993

The vibration damping of structure is increased by thermal actuator. The thermal actuator causes thermal stress across the section of structure. The several kinds of control theories are proposed and the proposed control theories are successful in increasing vibration damping. This scheme can be effectively applied to large space structure [LSS] having very low natural frequencies.

• Smart Structures and Systems
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• v.20 no.3
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• pp.329-342
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• 2017

In this paper, the dispersion characteristics of elastic waves propagation in sandwich nano-beams with functionally graded (FG) face-sheets reinforced with carbon nanotubes (CNTs) is investigated based on various high order shear deformation beam theories (HOSDBTs) as well as nonlocal strain gradient theory (NSGT). In order to align CNTs as symmetric and asymmetric in top and bottom face-sheets with respect to neutral geometric axis of the sandwich nano-beam, various patterns are employed in this analysis. The sandwich nano-beam resting on Pasternak foundation is subjected to thermal, magnetic and electrical fields. In order to involve small scale parameter in governing equations, the NSGT is employed for this analysis. The governing equations of motion are derived using Hamilton's principle based on various HSDBTs. Then the governing equations are solved using analytical method. A detailed parametric study is conducted to study the effects of length scale parameter, different HSDBTs, the nonlocal parameter, various aligning of CNTs in thickness direction of face-sheets, different volume fraction of CNTs, foundation stiffness, applied voltage, magnetic intensity field and temperature change on the wave propagation characteristics of sandwich nano-beam. Also cut-off frequency and phase velocity are investigated in detail. According to results obtained, UU and VA patterns have the same cut-off frequency value but AV pattern has the lower value with respect to them.

• Computers and Concrete
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• v.19 no.1
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• pp.1-6
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• 2017

Prestressed concrete I-girders are subject to different load types at their construction stages. At the time of strand release, i.e., detensioning, prestressed concrete girders are under the effect of dead and prestressing loads. At this stage, the camber, total net upward deflection, of prestressed girder is summation of the upward deflection due to the prestressing force and the downward deflection due to dead loads. For the calculation of the upward deflection, it is generally considered that prestressed concrete I-girder behaves linear-elastic. However, the field measurements on total net upward deflection of prestressed I-girder after detensioning show contradictory results. In this paper, camber calculations with the linear-elastic beam and elastic-stability theories are presented. One of a typical precast I-girder with 120 cm height and 31.5 m effective span length is selected as a case study. 3D finite element model (FEM) of the girder is developed by SAP2000 software, and the deflections of girder are obtained from linear and nonlinear-static analyses. Only geometric nonlinearity is taken into account. The material test and field measurement of this study are performed at prestressing girder plant. The results of the linear-elastic beam and elastic-stability theories are compared with FEM results and field measurements. It is seen that the camber predicted by elastic-stability theory gives acceptable results than the linear-elastic beam theory while strand releasing.